KS3 Maths · Year 7 · Chapter 16: Comparing data · Lesson 1

Grouped frequency tables

Year 7About 65 minutesNo calculator46 marks

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Date

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Quick questions to start.

A1
Needed today
Which of these times are in the class $20 < t \leq 30$ ? $20, 24.5, 30, 30.5$
[1 mark]
Answer
A2
Needed today
A pie chart shows $40$ people. How many degrees stand for one person?
[1 mark]
Answer
A3
Last lesson
Make $x$ the subject of $y = 2 x + 9$ .
[1 mark]
Answer
A4
From chapter 3
A bag holds $3$ red and $9$ blue counters. One is taken at random. Work out the probability that it is red.
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

These are the times, in minutes, that $18$ people waited for a bus.

$7$ , $13$ , $22$ , $4$ , $20$ , $9$ , $25$ , $11$ , $16$ , $3$ , $28$ , $14$ , $19$ , $8$ , $21$ , $12$ , $6$ , $27$

Complete the frequency table.

Hint Go through the list once, in order, and tick the class for each time.

20

goes in

10 < t \leq 20

, because that class includes

20

B1
These are the masses, in kg, of $15$ parcels.
$1.5$ , $3.2$ , $4.0$ , $0.8$ , $5.6$ , $2.0$ , $3.9$ , $4.7$ , $1.1$ , $2.6$ , $5.2$ , $3.4$ , $0.6$ , $4.4$ , $2.9$
Write down the three frequencies, in order.
[3 marks]
Answer

Example 2

The table shows the masses of $25$ eggs. Write down the modal class. One egg is picked at random. Work out the probability that it weighs more than $60$ g.

Hint The modal class has the highest frequency. For the probability, count the eggs in every class above

60

g and put that over the total.

B2
The table shows the lengths of $30$ phone calls. Write down the modal class. One call is picked at random. Work out the probability that it lasted more than $10$ minutes, in its simplest form.
[3 marks]
Answer

Example 3

At a party, $9$ people are aged $0 < a \leq 20$ , $15$ are aged $20 < a \leq 40$ , $8$ are aged $40 < a \leq 60$ and $4$ are aged $60 < a \leq 80$ . Work out the angle of each sector for a pie chart of the ages.

Hint A full circle is

36 0^{\circ}

, shared between

36

people.

B3
Of $40$ students, $6$ have heights $130 < h \leq 140$ cm, $14$ have $140 < h \leq 150$ , $12$ have $150 < h \leq 160$ and $8$ have $160 < h \leq 170$ . Work out the angle of each sector for a pie chart, in order.
[3 marks]
Answer

Example 4

These are the numbers of texts $20$ pupils sent in one day.

$3$ , $12$ , $7$ , $18$ , $0$ , $9$ , $14$ , $5$ , $11$ , $2$ , $6$ , $8$ , $13$ , $6$ , $19$ , $10$ , $12$ , $15$ , $1$ , $11$

Make a grouped frequency table with classes $0$ – $4$ , $5$ – $9$ , $10$ – $14$ and $15$ – $19$ . Why are these classes not written like $0 < n \leq 4$ ?

Hint A number of texts is always a whole number, so nothing falls between

4

and

5

B4
These are the numbers of books $18$ pupils read in a term.
$2$ , $9$ , $5$ , $11$ , $0$ , $7$ , $4$ , $13$ , $6$ , $3$ , $8$ , $10$ , $1$ , $5$ , $12$ , $7$ , $9$ , $6$
Using classes $0$ – $3$ , $4$ – $7$ , $8$ – $11$ and $12$ – $15$ , write down the four frequencies in order.
[3 marks]
Answer

Practice

Year 7

C1
The table shows the times $50$ runners took. Work out the missing frequency.
[2 marks]
Answer
C2
The table shows the times $40$ swimmers took. One swimmer is picked at random. Work out the probability that they took $30$ seconds or less.
[2 marks]
Answer

C3
Sam wants to know how long pupils at his school spend on homework each night. He asks $6$ pupils in his own top-set maths class. Give two reasons why this is not a good way to collect the data.
[2 marks]
C4
Ravi groups some heights into the classes $140$ – $150$ cm, $150$ – $160$ cm and $160$ – $170$ cm. Explain what is wrong with his classes.
[2 marks]

Exam-style questions

GCSE Foundation

D1
Ella puts the times $5$ , $10$ , $14$ , $20$ , $23$ , $17$ , $9$ and $28$ minutes into the classes $0 < t \leq 10$ , $10 < t \leq 20$ and $20 < t \leq 30$ . She says, "There are $4$ times in the class $10 < t \leq 20$ ."
Ella is wrong. Explain why, and give the correct frequency of each class.
[3 marks]
Answer

D2
These are the heights, in cm, of $24$ plants.
$12$ , $35$ , $8$ , $22$ , $27$ , $19$ , $31$ , $14$ , $26$ , $9$ , $18$ , $24$ , $33$ , $21$ , $16$ , $28$ , $5$ , $20$ , $29$ , $38$ , $13$ , $25$ , $30$ , $23$
(a)
Complete the frequency table. Write the four frequencies in order.
[2 marks]
Answer
(b)
The data is shown in a pie chart. Work out the angle of the sector for the modal class.
[3 marks]
Answer
Total for D2: 5 marks
D3
The table shows the ages of $60$ visitors to a museum.
(a)
What percentage of the visitors were older than $40$ ?
[2 marks]
Answer
(b)
One visitor is picked at random. Find the probability that they were $20$ or younger, in its simplest form.
[2 marks]
Answer
Total for D3: 4 marks
D4
The table shows the lengths of $40$ phone calls. In a pie chart of the data, the sector for $5 < t \leq 10$ is $10 8^{\circ}$ . There are twice as many calls in $10 < t \leq 15$ as in $15 < t \leq 20$ .
(a)
Work out the three missing frequencies. Write them in order.
[4 marks]
Answer
(b)
Work out the angle of the sector for $0 < t \leq 5$ .
[2 marks]
Answer
Total for D4: 6 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
$30$ pupils took a test. Their marks are grouped in the classes $0$ – $10$ , $11$ – $20$ , $21$ – $30$ and $31$ – $40$ . In a pie chart of the marks, the sectors for $0$ – $10$ and $11$ – $20$ are $7 2^{\circ}$ and $13 2^{\circ}$ . Three more pupils scored $21$ – $30$ than scored $31$ – $40$ . Work out the four frequencies.
[4 marks]
Hint 1 · What to try
How many degrees stand for one pupil?
Hint 2 · The first line
$360 \div 30 = 12$ , so $7 2^{\circ}$ is $6$ pupils.
Hint 3 · The full method
$30 - 6 - 11 = 13$ pupils are left for two classes that differ by $3$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can sort data into classes.
I can place a value on a class boundary.
I can find a modal class, angles and probabilities.
I can spot poor classes or a poor sample.

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